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Algebra Logika, 2010, Volume 49, Number 1, Pages 60–97 (Mi al429)  

This article is cited in 5 scientific papers (total in 5 papers)

Structure of the automorphism group for partially commutative class two nilpotent groups

V. N. Remeslennikov, A. V. Treier

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk, Russia

Abstract: Let $R$ be a ring, which is either a ring of integers or a field of zero characteristic. For every finite graph $\Gamma$, we construct an $R$-arithmetic linear group $H(\Gamma)$. The group $H(\Gamma)$ is realized as the factor automorphism group of a partially commutative class two nilpotent $R$-group $G_\Gamma$. Also we describe the structure of the entire automorphism group of a partially commutative nilpotent $R$-group of class two.

Keywords: automorphism group, partially commutative nilpotent group, arithmetic group, commutativity graph.

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English version:
Algebra and Logic, 2010, 49:1, 43–67

Bibliographic databases:

Document Type: Article
UDC: 512.544.43+512.544.33+512.547.4
Received: 24.08.2009

Citation: V. N. Remeslennikov, A. V. Treier, “Structure of the automorphism group for partially commutative class two nilpotent groups”, Algebra Logika, 49:1 (2010), 60–97; Algebra and Logic, 49:1 (2010), 43–67

Citation in format AMSBIB
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\paper Structure of the automorphism group for partially commutative class two nilpotent groups
\jour Algebra Logika
\yr 2010
\vol 49
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\pages 60--97
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\jour Algebra and Logic
\yr 2010
\vol 49
\issue 1
\pages 43--67
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Treier A.V., “Dva rezultata dlya gruppy avtomorfizmov chastichno kommutativnykh dvustupenno nilpotentnykh grupp”, Vestn. Novosibirskogo gos. un-ta. Ser.: Matem., mekh., inform., 10:2 (2010), 85–97  zmath  elib
    2. A. V. Treier, “Dva rezultata dlya gruppy avtomorfizmov chastichno kommutativnykh dvustupenno nilpotentnykh grupp”, Vestn. NGU. Ser. matem., mekh., inform., 10:2 (2010), 85–97  mathnet
    3. Ch. K. Gupta, E. I. Timoshenko, “Universal theories for partially commutative metabelian groups”, Algebra and Logic, 50:1 (2011), 1–16  mathnet  crossref  mathscinet  zmath  isi
    4. Duncan A.J. Remeslennikov V.N., “Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups”, Int. J. Algebr. Comput., 22:7 (2012), 1250074  crossref  mathscinet  zmath  isi  elib  scopus
    5. E. N. Poroshenko, “Universal equivalence of some countably generated partially commutative structures”, Siberian Math. J., 58:2 (2017), 296–304  mathnet  crossref  crossref  isi  elib  elib
  • Алгебра и логика Algebra and Logic
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